Evaluating the Stability of the Smogon Tier List for Competitive Pokémon Battling

Tier lists are often used to describe the relative power of different competitive game elements. These are used so that players can evaluate the relative power of certain aspects of a competitive game and act accordingly. In the game Pokémon, each Pokémon is assigned into a tier based on its power, performance in tournament play, and potential synergy with other Pokémon it could team with. These tier lists, however, are typically designed based on observation, meaning that their quality could suffer. In this work, we treat tier lists as coalition formation games. By doing this, we can leverage algorithms designed to find stable coalitions. In terms of tier lists, this would mean that each Pokémon would be in the correct tier and have no desire to move to a higher or lower tier. To evaluate this, we examine the Smogon tier list for Generation 1 Pokémon to determine its stability.